Validation of an Analytical Model for the Acoustic Impedance Eduction of Multi-Cavity Resonant Liners by a High-Fidelity LES Approach

The massive growth of the air traffic during the last years is leading to stricter limitations on the noise emission levels radiated from aircraft engines. To face this issue, the installation of acoustic liners on the intake duct and the exhaust nozzles is a common strategy adopted to properly abate the noise emissions coming from the fan, the compressor, the turbine, and the jet. In this context, the aim of the present paper is to use high-fidelity LES simulations to validate a MDOF (multi-degree of freedom) extension of the single- and double-degree of freedom (SDOF and DDOF) analytical model provided by Hersh for the eduction of the liner acoustic impedance. Firstly, the results of the original Hersh model are compared with LES calculations performed with the OpenFOAM suite on a single-orifice and single-cavity layout (SDOF). Then the extension of the Hersh model to multi-cavity (MDOF) geometries by using a recursive formulation is presented. Finally, high fidelity simulations are carried out for single-orifice and multi-cavity (MDOF) configurations to validate the method extension and to understand how the resonant coupling and the acoustic impedance are affected by multi-cavity resonant elements. The excellent agreement between the high-fidelity results and the analytical predictions for the single-cavity pattern confirms that the Hersh model is a useful formulation for the preliminary design of a SDOF acoustic liner. The model extension to MDOF configurations allows the designers to broaden the design space, and thus a validated analytical method is strictly necessary to perform sensitivity studies to the multi-cavity geometrical parameters (i.e., face-sheet thickness, cavities depth, porosity). Basically, a multi-cavity configuration makes the liner element resonate at different frequencies leading to multiple absorption peaks in the audible range. In this way, the acoustic performance of the liner is extended to a wider frequency range, overcoming the limitations of a SDOF configuration.